Commutative and Cost of capital: Difference between pages

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imported>Brianlenoach@hotmail.co.uk
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Broadly, the rate of return on a firm’s investments which is required to service the providers of the firm’s capital.
''Maths.''


The property that exchanging the ordering of maths operations makes no difference to final results.  
Often the term is used in a more specific sense to refer to the weighted average cost of capital of a business.




====Multiplication and addition are commutative====
For example if a firm's cost of capital is 8%, it must earn a return of at least 8% on its operational investments in order to provide the investors with the minimum investment return of 8% which they require.


The commutative property of multiplication means that exchanging the ordering of the items multiplied together makes no difference to the final result.


=====Example 1=====
The concept of cost of capital is important because when inferior rates of return are earned from operational investments - for example only 5% compared with a cost of capital of 8% - such operations are destructive of shareholder value and need to be improved or discontinued.
3 x 4 gives the same result as 4 x 3.


 
The results of these operations may appear (wrongly) to be profitable, when considered in simplistic historical cost financial accounting terms.  
In the first case:
 
3 x 4 = '''12'''
 
 
In the second case:
 
4 x 3 = '''12'''
 
 
 
=====Example 2=====
The commutative property also applies to addition.
 
4 + 5 gives the same final result as 5 + 4.
 
 
Both expressions give the result 9.
 
 
====Division and subtraction are not commutative====
 
The commutative property does not apply to division. The order of items being divided does make a difference to the final result.
 
=====Example 3=====
20 / 4 gives a different result from 4 / 20.
 
 
In the first case:
 
20 / 4 = '''5'''
 
 
In the second case:
 
4 / 20 = '''0.2'''
 
 
 
=====Example 4=====
The commutative property does not apply to subtraction.
 
5 - 3 gives a different result from 3 - 5.
 
 
The result of the first expression is '''+2'''.
 
The second expression produces '''-2'''.
 
 
 
=====Multiplication and addition are also associative=====
The [[associative]] and commutative properties apply both to multiplication and addition.
 
For this reason, they are sometimes mixed up, but they are different.




== See also ==
== See also ==
* [[Associative]]
* [[Discount rate]]
* [[Commutation]]
* [[Opportunity cost]]
* [[Distributive]]
* [[Opportunity cost of capital]]
* [[Denominator]]
* [[Shareholder value]]
* [[Numerator]]
* [[Tax shield]]
* [[Weighted average cost of capital]]


[[Category:The_business_context]]
[[Category:Corporate_finance]]

Revision as of 21:35, 13 December 2014

Broadly, the rate of return on a firm’s investments which is required to service the providers of the firm’s capital.

Often the term is used in a more specific sense to refer to the weighted average cost of capital of a business.


For example if a firm's cost of capital is 8%, it must earn a return of at least 8% on its operational investments in order to provide the investors with the minimum investment return of 8% which they require.


The concept of cost of capital is important because when inferior rates of return are earned from operational investments - for example only 5% compared with a cost of capital of 8% - such operations are destructive of shareholder value and need to be improved or discontinued.

The results of these operations may appear (wrongly) to be profitable, when considered in simplistic historical cost financial accounting terms.


See also

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